Hope Powell cut a relieved figure last night as her England team, having performing poorly in the first hour of their second group match, came from behind to put themselves within touching distance of a place in the World Cup quarter-finals.

Following a 1-1 draw with Mexico in their opening group game, they went behind in Dresden to an 18th-minute Sarah Gregorius goal and their prospects were looking grim until the midfielder Jill Scott equalised in the 63rd minute. They had been in control for much of the second period, however, and the substitute Jess Clarke's 81st-minute victory clincher was deserved after a determined fight-back.

The result at the Rudolf-Harbig-Stadion, combined with Mexico's 4-0 defeat by Japan in Leverkusen yesterday, means that a five-goal swing is needed if the Mexicans are to edge past England. That's an unlikely scenario, but Powell is taking nothing for granted.

"We haven't got out of the group by any stretch of the imagination," she insisted. "We enjoy making these tournaments hard work. Credit to New Zealand, they really put us on the back foot and we struggled in the first half, but I think we had most of the opportunities and play.

"We haven't quite hit that mark yet, though. I'm hoping today's result might give us some confidence, but there's lots of room for improvement – I know that and the players know that."

Hesitant defending led to New Zealand's goal, Gregorius squeezing between two players to stab the ball over the line. And if Gregorius had not stumbled when clear seven minutes before the interval, England would have been in desperate trouble.

They showed a marked improvement after the break, however, and after Jill Scott had neatly glanced home, Clarke hit an eight-yard drive into the roof of the net to clinch victory. England now face Japan. Powell said: "We are expected to get out of the group but we are not quite there yet. We've got another game to go, and it's going to be a tough game."